In this paper we address the chattering phenomenon which is a common drawback associated with the normal Sliding Mode Control (SMC) law for a basic shape memory alloy (SMA) actuated system. A new method has been proposed to counter this effect by combining the concepts of Fast Terminal SMC and Dynamic controller. A phenomenological model is developed for the SMA which incorporates a piecewise linear hysteresis behavior. This model is used for both open loop as well as closed loop simulations for a linear motion control system. Based on this model, a dynamic terminal sliding mode control law is derived and applied to the system. A normal SMC law with saturation function which is known to reduce chattering is compared with the proposed control law for its effectiveness to curb the issue of chattering versus its ability to faithfully track a desired trajectory. Numerical Simulations indicate that the proposed law is able to reduce the chattering effect sufficiently and at par with the control technique involving saturation function.